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摘要
In this paper, based on actual road networks, a model of the non-homogeneous double weighted fractal networks is introduced depending on the number of copies s and two kinds of weight factors w(i), r(i) (i = 1, 2,...,s). The double-weights represent the capacity-flowing weights and the cost-traveling weights, respectively. Denote by w(ij)(F) the capacity-flowing weight connecting the nodes i and j, and denote by w(ij)(C) the cost-traveling weight connecting the nodes i and j. Let w(ij)(F) be related to the weight factors w(1), w(2),...,w(s), and let w(ij)(C) be related to the weight factors r(1), r(2),...,r(s). Assuming that the walker, at each step, starting from its current node, moves to any of its neighbors with probability proportional to the capacity-flowing weight of edge linking them. The weighted time for two adjacency nodes is the cost-traveling weight connecting the two nodes. The average weighted receiving time (AWRT) is defined on the non-homogeneous double-weighted fractal networks. AWRT depends on the relationships of the number of copies s and two kinds of weight factors w(i), r(i)(i = 1, 2,...,s) The obtained remarkable results display that in the large network, the AWRT grows as a power-law function of the network size N-g with the exponent, represented by theta = log(s)(w(1)r(1) + w(2)r(2) + ... + w(s)r(s)) < 1 when w(1)r(1) + w(2)r(2) + ... + w(s)r(s) not equal 1, which means that the smaller the value of w(1)r(1) + w(2)r(2) + ... + w(s)r(s) is, the more efficient the process of receiving information is. Especially when w(1)r(1) + w(2)r(2) + ... + w(s)r(s) = 1, AWRT grows with increasing order N-g as log N-g or (log N-g)(2). In the classic fractal networks, the average receiving time (ART) grows with linearly with the network size N-g. Thus, the non-homogeneous double-weighted fractal networks are more efficient than classic fractal networks in term of receiving information.
- 出版日期2017-5-1
- 单位江苏大学
